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Sunday, July 01, 2007

On Physics, Mathematics, Time and Space

Physics has managed to explain most of our surroundings through the Laws and Theorems we learn now in school. But the unlearned student might ask to himself, why do such laws exist? Who invented such laws and how did he imprint the upon reality?First of all, the Laws & Theorems of physics (or chemistry, mechanics...) are not laws by which reality moves. They are laws by which we UNDERSTAND and PREDICT reality. This is a common misconception and needs to be clarified.However, a now not-so-unlearned student might ask: Well, if Laws & Theorems describe the properties of the Universe, where did such Properties come from (notice the capitalization)?Enter Emmy Noether, 1981.Noether showed that the principle of energy conservation follows from symmetry under time translations. See the article below for further explanation if you're interested, but for the layman I present a simple version:Imagine a sphere, a perfect sphere, the rotational symmetries od a sphere single out no particular direction while it rotates (i.e. with no further frame of reference, the sphere can not be said to rotate in any one particular direction or speed). Extrapolate this metaphore to time and you'll get the point on what symmetry under time variation means. From this, its all mathematics. What this means is, that the principles of energy and mass conservation follow naturally from a Universe that appeared from an initial state in which there was no matter- from nothing.Ours is such a Universe.I can already hear comments like "Hey, what about the Big Bang?" "If there's no matter in the Universe how come we exist?".This doesn't really disagree with the Big Bang and all things that follow from it.Consider the following:Energy conservation follows from the symmetries that exist naturally in an empty void. So, if there was nothing, mass cannot exist right now, because it couldn't have been created out of nothing right?

Wrong

It can be created as long as the balance of mass and energy remains constant. Measurements have confirmed that the sum of all mass observed equals exactly to the negative gravitational energy. This is one of the explanations of the relationship between gravity and mass, although I am no expert on this matter, so I'll leave it at that.

Ergo, everything matches up.

There is another interesting point from Noether's article. She also states that because of the mathematics involved in the demonstration, in regions of spacetime near gravitating sources, where the Riemann curvature is non-vanishing, there is failure of a principle of local energy conservation. The energy balance locally cannot be discussed independently of the coordinates one uses to calculate it, and consequently different results are obtained in various different coordinate frames. Be on the watchout for a post on Relativity on this blog